Can a Very Short External Threaded Fastener Pass Completely Through a No Go Ring Gage and Still Pass Inspection?

The Answer is Yes!

Reference ANSI/ASME B1.2, 1983, page 128, within paragraph 5.2.1. It reads as follows: NOT GO (LO) functional diameter is acceptable when the NOT GO (LO) thread ring gage applied to the product external thread does not pass over the threads more than three turns. The gage should not be forced. Special requirements such as exceptionally thin or ductile material, small number of threads, etc. may necessitate modification of this practice.

What Does Modification of this Practice Mean?

A short-threaded fastener with four threads or less may enter beyond three turns when the threaded length is too short to permit the fastener to stop within three full revolutions of engagement because none of the threads are fully formed.
For example, when you have a short-threaded fastener, such as a 4-40 x 3/32 socket set screws with a cup point. This part has less than four threads when you subtract the chamfer angle on the point end of the screw. This leaves you with 3 threads of which none are fully formed because they are considered lead threads. Socket Set Screws are allowed four incomplete lead threads. Two on the point end and two on the socket end. As a result, allowing very little resistance to stop the part from entering the NO GO GAGE more than three turns. This is a typical example of what Modification of this Practice Means.